| Project/Area Number |
23650005
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | Nagaoka University of Technology |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | フーリエ解析 / 対称群 / 回転群 / 二面体群 / 調和解析 / フィルタ / 学習 / 指標 / 表現論 / アルゴリズム / サンプリング / 群論 / 機械学習 |
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| Research Abstract |
As a step toward establishment of the way to extract a hidden procedure by using non-commutative harmonic analysis, this research presented several methods which extract some important features of signals defined over a non-commutative group from their Fourier expansion, such as: (1) A method which operates a given signal over a dihedral group in its frequency domain, by an efficient convolution (2) An interpolation method which transform the domain of a signal which is a discrete mesh in the3-dimensional rotation group into a more finer mesh, exploiting the concentration of the contribution from smooth component of the signal to certain components in the frequency domain (3) A method that provides a quantitative measure representing to what extent a function over the group of permutations of n objects is affected by the change of the labeling of objects by 1, 2, ..., n.
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